EECS 215 Exam 2 Fall 2007 solutions

EECS 215 Exam 2 Fall 2007 solutions - EECS 215 Fall Term...

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Unformatted text preview: EECS 215 Fall Term 2007 Midterm Exam 2 Name: 50M fig/75 . ___.._____ Lecture Section Te m Rules: Monday, November 19, 2007, 6:00 to 7:30 PM nominal exam time. l. 2. Closed Book, etc. 3. 2 Sides (8.5”xl 1”) of notes allowed 4. Calculators Needed and Allowed. No devices with full alphanumeric keyboards are permitted. 5. Exam is given under the College of Engineering Honor Code principles and practices. 6. No communications of any kind are allowed. Use of cell phones, cameras, personal data assistants, computers, or any other electronic devices, besides approved calculators, will be treated as an Honor Code violation. 7. Work to be done in Exam booklet. Turn in all pages of the exam. Do not unstaple the pages. 8. DO NOT WRITE ON THE BACK OF PAGES. Work on backs of pages will NOT be graded. 9. Show your work and briefly explain major steps to maximize partial credit. (for example: i3=il+i2, node A, KCL). NO CREDIT WILL BE GIVEN IF NO WORK IS SHOWN. 10. WRITE YOUR FINAL ANSWERS IN THE AREAS PROVIDED This Exam Contains 4 problems over 15 pages (including ample workspace). Sign the College of Engineering Honor Code Below. N 0 credit will be iven for the exam without a si I have neither given nor received aid on this examination. Signed: Do not write below this line A************************************************************************ Problem 1 [a b ] Problem 2 [ ] Problem 3 [ ] Problem 4 [ ] Problem 1: Transistors 125 points) Assume we have a linear-square law MOSFET in the circuit shown below. The transistor follows the rules: KB VGS — VT)VDS ~~;~ V025] if V05 2 (VT + % VHS] and VDS S (KW ~ ) Linear / Trim/e l 1,) : 5K(Vm — VT )2 if VHS 2 and VHS 2 (VGS ~ VT) Saturation O ()Ihe/wise a) For the circuit above, find closed form, analytic expressions for Vom, V05, V95, and the small signal gain G as functions of Vin and the known constants assuming that the transistor is runnin in saturation mode. (15Points) VGs: V; '1 Vow: [YE—ED: _ B5: [Mr VT): 75’» + #1 Workspace for (a) VI) D Additional Workspace for (a) VDD For the remainder of the problem, assume the following values: ~1< =3mA/V2 VT =+l.5V R, =5KQ R2 = 101m VDD =+15V b) Over what V," range is the transistor in saturation? Also, what are the bounds on Vow (when the transistor is in saturation)? In your work, make it clear how you derive your answer (10 points) VDD . Transistor is in saturation for: __L__5___X SVinS M L Event: “Lg‘iv For {acre/5m? V9,, transistor 40¢: Fro», off- a sin; Him 541" a linear OFF 62% I 0;; Far 10,5 4 V13 0/ (/m < V1. turn: an 4* Vin: l/r: I.5’\/ (Magma/mg Vaur 5 Egg ‘ 3%(7'5'l'5)3.— )JV ’Bk*7’27< 547" 9 (med/’9 Winn V95 5 VM'VI’ VQflf : l/ifi " VT‘ n— . p [f " (Wn'l/r>fl/(f'+{§a> -— l/.n VT SJVC 5/ V“, Vznl(k/,)+ M‘q(‘é;+kLl'/¢Vr)+[: ‘4?" 1—% Vr1 ‘ w (3;) + v», %— +¢ -3//-5))+[-.g:+ s; (as): 4.5/1; + W» =' 2.8I3 1/ Vac/f k f‘ a. Problem 2: First Order Circuit 130 points! The inductor circuit below has a steg [unction current source, as well as a switch that changes from position “a” to position “b” at time t = 2 ms. Calculate the inductor current labeled iL for time t>0, writing in the space provided. (312) ix 2 u(t)A 12.0 . 2x : — 2L 3 0 00 tW/(Pffi/MT f < O W 541%: l (or c hark WW; KZL/m/L) A(t >2ms) additional work space for problem 2 (312) ix : 2.0 a b fill t=2ms 2wvA T 40 36 mH 12 n iL l 21w= 2: Ir 455:9” 1:,- : 3/] [:- 24,) VT : I-r/4)+3Ir + .717 :: 9y RT”: l/T/fr 7-: 952’ 1572'” T 1., _ _ “1/ “n'Bb-ZJL LLH'): “(20:39: t 7’: 1:. inf/ch 2,115) = 0.6/2 e 4/3”“ Problem 3: Second Order Circuit — Initial Conditions (20 Points) Note: Problems 3&4 Use the same circuit & values, we suggest reading both problem before starting. The circuit below has the switch in position “a” for a long time, with the capacitor discharged. At time t=0, the switch is moved to position “b”. Determine the initial and final conditions for the capacitor and inductor, and record in the table provided. You must show the work that got you to these answers in order to receive credit. Be certain to pay careful attention to defined voltage polarities and current reference directions. Also recall that lnF = 10'9 F. 400 {2 20V 10V Variable t= 0' = OJr * t —-) oo vc 0V .9 0 V V [C O O u 0 «14.04 V O _. a 10.34m,4-;/0.34/m4 o _L m (00‘1 v2 (0‘9 (ti/1‘ (hi/)4! 1.457%; fang”: [y CJO’): {a (0 f) l¢(0')=?c(¢v)=0 0 7C (o')= meow * ll Workspace for problem 3 {Ca—5L: dawn/ii kVL‘. “Va +W+{L(4aa)+MV-70 0 +VL+(I0-14M)[400)"/0=p 1/7,“: “14.067 I/ Problem 4: Second Order Circuit - Solution {25 Points) Now examine the circuit in problem 3, but with different values for the voltage sources. The initial conditions for the capacitor are provided in the table below. Determine the value for the capacitor voltage vdt) for time t>0, and write in the space provided. 400 [2 20V 10V l3 workspace for problem 4 20V 10V .I a “if “is A. “fladwoe “'4” 6 am ,4 mar) @[ :54”? .1 a 0C t: c 717 ’ A; a Z": 14 [£139 «4 -= "/0240"? 5 I04 -—/ I é Ir ’40/tla’9F 7%)! I a) 4, 5 1,024 #05 W5 14 ...
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This test prep was uploaded on 04/04/2008 for the course EECS 215 taught by Professor Phillips during the Winter '08 term at University of Michigan.

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EECS 215 Exam 2 Fall 2007 solutions - EECS 215 Fall Term...

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